# How do you combine (x+2)/(5x^2)+(x+4)/(15x)?

Jul 17, 2016

$\frac{{x}^{2} + 7 x + 6}{15 {x}^{2}}$

#### Explanation:

Adding fractions requires a common denominator.

The LCD is $15 {x}^{2}$

An equivalent fraction for each fraction must be found with the denominator $15 {x}^{2}$

$\textcolor{m a \ge n t a}{\frac{x + 2}{5 {x}^{2}}} + \textcolor{b l u e}{\frac{x + 4}{15 x}}$

$\textcolor{m a \ge n t a}{\frac{x + 2}{5 {x}^{2}} \times \frac{3}{3} = \frac{3 \left(x + 2\right)}{15 {x}^{2}}}$

$\textcolor{b l u e}{\frac{x + 4}{15 x} \times \frac{x}{x} = \frac{x \left(x + 4\right)}{15 {x}^{2}}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{m a \ge n t a}{\frac{x + 2}{5 {x}^{2}}} + \textcolor{b l u e}{\frac{x + 4}{15 x}}$

=$\textcolor{m a \ge n t a}{\frac{3 \left(x + 2\right)}{15 {x}^{2}}} + \textcolor{b l u e}{\frac{x \left(x + 4\right)}{15 {x}^{2}}}$

= $\frac{\textcolor{m a \ge n t a}{3 x + 6} + \textcolor{b l u e}{{x}^{2} + 4 x}}{15 {x}^{2}}$

= $\frac{{x}^{2} + 7 x + 6}{15 {x}^{2}}$